Ghiby Wrote:
I would need at least 15 influence points to do what I'd like to, but I'm so far away that I think I'll never reach that level

You misunderstand the concept and hence make some false assumptions. Influence is not an expandable resource. Instead, it represents a threshold you have to overcome. Or, in other words, you need to be influential enough in order to make fundamental changes in your states organization/society.

Your influence may increase or decrease as a result of a reform, but it is not used as payment in any form. If, for example, you are lucky and your influence would be slightly above 7, you could implement 3 reforms at the cost of 7 influence in 3 consecutive quarters.

Ghiby Wrote:
so, other than waiting to have the influence incrementally increased over time, is anything else I can do on my end, to increase the regent's influence at a faster pace?

Due to the strong link between happiness and influence, you can try to make your citizens as happy as can be ...